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Simple Analytical Expression (simple + analytical_expression)
Selected AbstractsGeneral Steady-State Shape Factor for a Partially Penetrating WellGROUND WATER, Issue 1 2010Vitaly A. Zlotnik We present the closed form of a general steady-state shape factor for a partially penetrating well in a uniform anisotropic aquifer. Our simple analytical expression for the shape factor has a uniform representation for full range of parameters and meets or exceeds the accuracy of previous results obtained through semiempirical methods (e.g., Bouwer and Rice [1976] equations). This general shape factor pertains to the flow of fluids (water or air) in subsurface formations when the upper formation boundary has constant potential and the lower boundary is impermeable. The results of our investigation are directly applicable to analyses of (1) slug tests with falling or rising head and (2) injection/extraction tests with constant head, essential techniques for the characterization of hydraulic conductivity of aquifers, streambeds, or lakebeds as well as the design of aquifer and soil remediation systems. [source] Reciprocal-space mapping of epitaxic thin films with crystallite size and shape polydispersityACTA CRYSTALLOGRAPHICA SECTION A, Issue 1 2006A. Boulle A development is presented that allows the simulation of reciprocal-space maps (RSMs) of epitaxic thin films exhibiting fluctuations in the size and shape of the crystalline domains over which diffraction is coherent (crystallites). Three different crystallite shapes are studied, namely parallelepipeds, trigonal prisms and hexagonal prisms. For each shape, two cases are considered. Firstly, the overall size is allowed to vary but with a fixed thickness/width ratio. Secondly, the thickness and width are allowed to vary independently. The calculations are performed assuming three different size probability density functions: the normal distribution, the lognormal distribution and a general histogram distribution. In all cases considered, the computation of the RSM only requires a two-dimensional Fourier integral and the integrand has a simple analytical expression, i.e. there is no significant increase in computing times by taking size and shape fluctuations into account. The approach presented is compatible with most lattice disorder models (dislocations, inclusions, mosaicity, ,) and allows a straightforward account of the instrumental resolution. The applicability of the model is illustrated with the case of an yttria-stabilized zirconia film grown on sapphire. [source] Influence of Ohmic diffusion on the excitation and dynamics of MRIASTRONOMISCHE NACHRICHTEN, Issue 1 2010M.J. Korpi Abstract In this paper we make an effort to understand the interaction of turbulence generated by the magnetorotational instability (MRI) with turbulence from other sources, such as supernova explosions (SNe) in galactic disks. First we perform a linear stability analysis (LSA) of non-ideal MRI to derive the limiting value of Ohmic diffusion that is needed to inhibit the growth of the instability for different types of rotation laws. With the help of a simple analytical expression derived under first-order smoothing approximation (FOSA), an estimate of the limiting turbulence level and hence the turbulent diffusion needed to damp the MRI is derived. Secondly, we perform numerical simulations in local cubes of isothermal nonstratified gas with external forcing of varying strength to see whether the linear result holds for more complex systems. Purely hydrodynamic calculations with forcing, rotation and shear are made for reference purposes, and as expected, non-zero Reynolds stresses are found. In the magnetohydrodynamic calculations, therefore, the total stresses generated are a sum of the forcing and MRI contributions. To separate these contributions, we perform reference runs with MRI-stable shear profiles (angular velocity increasing outwards), which suggest that the MRI-generated stresses indeed become strongly suppressed as function of the forcing. The Maxwell to Reynolds stress ratio is observed to decrease by an order of magnitude as the turbulence level due to external forcing exceeds the predicted limiting value, which we interpret as a sign of MRI suppression. Finally, we apply these results to estimate the limiting radius inside of which the SN activity can suppress the MRI, arriving at a value of 14 kpc (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Recognition of resonance in long radial transmission lines with static VAR compensation using travelling wavesEUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 1 2005Ljubivoje M. Popovi Abstract This paper presents an analytical procedure for estimation of resonance frequencies in long-distance radial transmission lines with static VAR compensation. The development of the procedure is based on a new approach in solving this problem. It employs the fact that the phenomenon is characterized by an algebraic sum of travelling current waves at the beginning of the line. Relatively simple analytical expressions are obtained by considering the phase angles of only one direct and only one corresponding reflected wave. Besides enabling a simpler and faster solution of the problem under various realistic conditions, the obtained analytical expressions also offer more direct analytical insight into the interplay of basic parameters. Copyright © 2005 John Wiley & Sons, Ltd. [source] | ||||||||||